According to US media reports, Arkhouse Management and Brigade Capital have recently submitted a proposal to acquire the chain for $21 per share, compared to Friday's closing price of $17.39.
This represents a more than 2% increase for the day and a 1.8% increase for the week, valuing Macy's at $4.77 billion.
The Wall Street Journal suggests that the $21 per share offer values the retailer at $5.8 billion.
While this price is 32% above Friday's closing price, it remains well below the stock's $70 high in 2015. The bid was made on December 1, and Macy's board and management remained silent on the issue throughout the past week.